Zimbabwean election officials count ballot papers after the close of voting on a referendum in Harare, on March 16, 2013. Zimbabweans voted on Saturday in the referendum expected to endorse a new constitution that would trim presidential powers and pave the way for an election to decide whether Robert Mugabe extends his three-decade rule. (PHILIMON BULAWAYO/REUTERS)

Zimbabwean election officials count ballot papers after the close of voting on a referendum in Harare, on March 16, 2013. Zimbabweans voted on Saturday in the referendum expected to endorse a new constitution that would trim presidential powers and pave the way for an election to decide whether Robert Mugabe extends his three-decade rule.(PHILIMON BULAWAYO/REUTERS)

It was seen as Zimbabwe’s new beginning: a constitution that would finally limit the powers of the autocratic president, Robert Mugabe, and set the nation on a course for free elections this summer.

But instead, for many Zimbabweans, the new era was the same as the old. A constitutional referendum on the weekend was marred by an embarrassingly low voter turnout, a police raid on an opposition office, and the arrest of a prominent human-rights lawyer.

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The constitution is almost certain to be approved, with early results showed an overwhelming “Yes” vote. But there is widespread cynicism among Zimbabweans about whether the vote will change anything in a country that Mr. Mugabe has dominated for the past 33 years.

Less than a third of the 6.6 million registered voters went to the polling stations to cast votes on Saturday. And a day later, Zimbabwean police continued their repressive tactics, arresting four senior aides of Mr. Mugabe’s main political rival, Prime Minister Morgan Tsvangirai, and then arresting a respected human-rights lawyer when she arrived at the scene.

The new constitution, while seen as a step forward, is unlikely to make much difference to the human rights abuses. It would still allow Mr. Mugabe to rule the country for two more five-year terms – until he is 99 years old.

The proposed new constitution includes a bill of rights, a constitutional court, and some limits on presidential power, including a requirement that two-thirds of parliamentarians must approve any declaration of emergency rule or dissolution of parliament. Presidential decrees would need to be supported by a majority of cabinet ministers.

But the Zimbabwean police, along with thuggish militias loyal to Mr. Mugabe, have often viewed themselves as above the law, and there is no sign that this would stop. In the lead-up to the referendum, some of Mr. Tsvangirai’s supporters were violently attacked, and the police raided at least four civil-society groups, seizing equipment and documents and detaining some of their employees.

In one of the most disturbing moves, the police have also seized the cheap hand-cranked radios that some local organizations were distributing in Zimbabwe to bypass the state broadcasting monopoly. The radios were intended to allow voters to get independent media reports, but the police declared them illegal.

On Sunday, the police arrested Mr. Tsvangirai’s chief legal adviser, Thabani Mpofu, and three members of his personal staff. When prominent lawyer Beatrice Mtetwa arrived at Mr. Mpofu’s home to help him, she reportedly took photos of the police and asked them to produce a search warrant – and was promptly handcuffed and taken to a police station, accused of “obstructing justice.”

Education Minister David Coltart, a member of Mr. Tsvangirai’s party in the coalition cabinet, said the arrest of Ms. Mtetwa was an intimidation tactic. Rather than obstructing justice, she was actually “obstructing injustice,” he wrote on his Twitter account.

The British ambassador to Zimbabwe, Deborah Bronnert, said the referendum was “a great day” but the reported arrests were “shocking.”

The referendum, which followed a marathon three-year effort to draft a new constitution, is seen as a crucial step towards the next Zimbabwean election, tentatively expected in July. Regional diplomats had insisted on the new constitution as a precondition for their support of the next election.

But while the referendum on Saturday was largely free of violence, the continuing wave of arrests of opposition supporters and human rights activists is an ominous sign for the upcoming election. The last election, in 2008, was so chaotic and violent that Mr. Tsvangirai dropped out of the second round of voting, even though he had won the first round. Hundreds of his supporters were killed, raped or assaulted by pro-Mugabe militias.

Election observers from Southern Africa said the referendum was “peaceful and credible.” But Mr. Mugabe banned Western observers from monitoring the referendum, and he has said he will do the same in the upcoming election.

Official results of the referendum are to be announced within five days.